Anomalous anharmonicity in doped cuprate superconductors

Strong nonlinear elastic effects arise due to the Lifshitz transition associated with a change in the Fermi surface topology. It is shown that an electronic contribution to the elastic characteristics of cuprates becomes important if the chemical potential is near but not too near the Van Hove critical energy $\epsilon_c$. In the case of a saddle point singularity in the energy spectrum an enhancement factor arises for the "electronic" anharmonic constants of the 3rd and 4th order, that is proportional to $\epsilon_F/(\epsilon_F-\epsilon_c)$ to the 1st and 2nd power, respectively. The behaviour of the Grueneisen coefficient in the vicinity of the Lifshitz transition is considered.